SOLUTION: determine the value of k for which the system of linear equations has infinitely many solutions. then find all the solutions corresponding to this value of k
3x+4y=12
x+ky=4
Algebra.Com
Question 1106903: determine the value of k for which the system of linear equations has infinitely many solutions. then find all the solutions corresponding to this value of k
3x+4y=12
x+ky=4
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
3x+4y=12
x+ky=4
In order for the two equations to have infinitely many solutions, the equations must be equivalent. Multiply the second equation by 3; now the two equations are
3x+4y=12
3x+3ky=12
For the equations to be equivalent, we must have equal coefficients for y: 3k=4; so k = 4/3.
I will guess that by "listing all solutions" you are looking for parametric equations. To get them, solve the equation for y and then use x as the parameter:
3x+4y = 12
4y = -3x+12
y = (-3/4)x+3
The parametric equations representing all solutions are
x = t
y = (-3/4)t+3
RELATED QUESTIONS
Determine the value of k for which the system of linear equations
2x + 5y = 10
x + (answered by josgarithmetic)
] Find all values of a for which the following linear system:
a) has no solution,... (answered by Alan3354)
Determine whether the system of linear equations has one and only one solution,... (answered by mananth)
x + 2y -3z = 0
3x + 4y + hz = 0
2x +3y + 2z = 0
Give the value of h for which the... (answered by richwmiller)
If the pair of limear equations 13x + ky= k and 39x+6y = k+4 has infinitely many... (answered by Alan3354)
Determine the value of k for which the system of linear equations
2x−y =5
6x+ky=2
(answered by MathLover1)
find all the value/s of k so that the system x+y=2 and x+(k^2 -3)y=k has
a) no solution
(answered by solver91311)
Determine whether the system of linear equations has one and only one solution,... (answered by stanbon)
Determine whether the linear system has one solution, no solution, of infinitely many... (answered by MathLover1)